In theory, international civil servants at the United Nations are prohibited from continuing to draw salaries from their own governments; in practice, however, some governments merely substitute living allowances for their employee's paychecks, assigned by them to the United Nations.
(A) for their employee's paychecks, assigned by them ( this sentence wrongly suggests that paychecks were assigned by the government to the UN, thus, changing the meaning. )
(B) for the paychecks of their employees who have been assigned (correct; sentence uses correct modifier "who" to modify the employees working for the UN; the sentence means that living allowances were substituted for paychecks of their employees- employees who were assigned to the UN)
(C) for the paychecks of their employees, having been assigned ( modifier error, having been doesn't correctly modify employees )
(D) in place of their employee's paychecks, for those of them assigned (this sentence incorrectly means that paychecks were assigned to the UN and the use of "them" creates confusion is them refereeing to the paychecks, government or employees? )
(E) in place of the paychecks of their employees to have been assigned by them(Who?) ( doesn't make sense)